Functional principal component analysis [1]}, [2]} is the cornerstone for many functional data analysis methods. To reduce the computation cost of FPCA over a large dataset, we develop a randomized algorithm for FPCA in Section REF . To retain the most relevant principal subspace information after subsampling, we propose the functional principal subspace sampling (FunPrinSS) probability in Section REF . Then, based on the operator perturbation theory in Section REF , the FunPrinSS probability is justified and an error bound is derived for our randomized FPCA in Section REF . A practical implementation of our algorithm is discussed in Section REF .
